Advertisement

Advertisement

The indefatigable in pursuit of the insoluble?

By VINCENT KIERNAN

IF nothing else, Andrew Wiles scores points for tenacity: the mathematician
says he has resolved a 17th-century mathematical puzzle. Last year he claimed
the same thing, only to have other experts point out the error of his
ways.

Wiles says he has cracked Fermat’s last theorem – its proof has been one of
the holy grails of mathematics since it was set out by Pierre de Fermat (1601-
1665). In a handwritten notation in a book, discovered after his death, Fermat
claimed that he had shown that the equation xn &plus; yn
&equals; zn has no integer solutions when n is greater than 2 and
x, y and z are numbers other than zero. (When n&equals;2, the formula becomes
the Pythagorean theorem familiar to schoolchildren, which does have integer
solutions.)

In June last year, Wiles, who is based at Princeton University in New
Jersey, announced at a conference in Britain that he had proved that Fermat
was right (New Scientist, Science, 3 July 1993). The announcement caused great
excitement. But by the end of the year, Wiles was forced to concede that the
final piece of his proof was defective.

On 24 October, Wiles began to dispatch copies of a new proof to colleagues
by Federal Express. He says he has fixed the flaw in a new proof fashioned
with the help of Richard Taylor, one of his former students who works at the
University of Cambridge. But it is likely to be several months before
mathematicians have probed the documents deeply enough to determine whether
Fermat can finally rest in peace.